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BOOK REVIEW 1089 and All That – A Journey into Mathematics by David Acheson, Oxford University Press, 2002, pp 178, £12.99, ISBN 0-19-8516231. This book is an ideal present for friends and relatives who are not mathematicians, but have enough curiosity to spend a gentle afternoon trying to find out what mathematics is about. It is also an ideal stocking filler for bright adolescents. The author gives an attractive tour of some proper mathematics from an elementary perspective. The title of this slim but sturdy volume is a homage to Sellar and Yeatman’s 1066 and All That, which in 1964 I thought was the funniest book ever written. This genre includes Willans and Searle’s Molesworth ouevre, and it is no accident that Molesworth surfaces in the book under review. Molesworth’s world is a close parallel of my daily life in 1964; lessons on mostly dull subjects were given by masters who ranged from the kind through to the grotesque and psychopathic. The tragedy of Molesworth was that he did not understand that mathematics was not a subject, but rather an extension of play. When the bell rang and masters tried to teach something dull, all you had to do was to put on a studious expression, and allow break to continue in your head. On the inside you could muck around with polygons, surds, quadratics and prime numbers. Having missed the key point about what it is to be human, it is no wonder that Molesworth became bitter. Now, one must approach books of mathematics popularization with extreme caution. They are prone to diverse faults. For example, they may sell more copies in a week than one’s own books will sell in a lifetime. Success is not something easily forgiven in a colleague. Moreover, parts of this book are extremely funny. How will Acheson live this down? There is a category of mathematical popularization (not this book) which is intellectually degenerate; this is when the author takes a phenomenon in the material world (waves, fish, planets, etc.) and pretends that because a piece of applied mathematics is effective at modelling some aspect of the phenomenon in question, then by looking at a glossy picture of the reality the reader (or more accurately the viewer) has access to the mathematics. You might as well try to experience music by looking at a picture of an orchestra. It may be true that a picture is worth a thousand words, but that merely serves to underline the tiny value of the word (the Yen of intellectual exchange). Look at the relationship between mathematics and reality the other way (but privately). There is sense in admiring the efforts of this particular material world to model perfect mathematical reality. Acheson’s Indian Rope Trick is a case in point. A sequence of linked rods will stand upright and stable if one end is vibrated sufficiently quickly. This is a beautiful mathematical result, and we should ruffle reality behind the ears for managing to emulate it. Buy this book. Geoff Smith
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